The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom. Here are the results

No, not mutually exclusive.

79/80

Answer: P (B|G) = 3/5 = 0.6

the probability that the guest is the friend of bride, P (bride | groom) is 0.6

Complete Question:

The usher at a wedding asked each of the 80 guests whether they werea friend of the bride or of the groom. The results are: 59 for Bride, 50 for Groom, 30 for both. Given that the randomly chosen guest is the friend of groom, what is the probability that the guest is the friend of bride, P (bride | groom)

Step-by-step explanation:

The conditional probability P (B|G), which is the probability that a guest selected at random who is a friend of the groom is a friend of the bride can be written as;

P (B|G) = P (B∩G) / P (G)

P (G) the probability that a guest selected at random is a friend of the groom.

P (G) = number of groom's friends/total number of guests sample

P (G) = 50/80

P (B∩G) = the probability that a guest selected at random is a friend is a friend of both the bride and the groom.

P (B∩G) = number of guests that are friends of both/total number of sample guest

P (B∩G) = 30/80

Therefore,

P (B|G) = (30/80) / (50/80) = 30/50

P (B|G) = 3/5 = 0.6